Communication channel

In wireless communications, a communication channel includes channel coefficients such as gain and phase factors as well as noise factors. For the one-tap linear model, we assume that the channel coefficients and the noise signal are given as $h$ and $n$, respectively. Then, the received signal at the receiver is represented as

$r = P h x + n$

where $x$ is the transmission signal at the transmitter and $P$ is the transmission power.

Rayleigh Fading Channel

When a fading model of given wireless channel can be represented as Rayleigh distribution, we model both the complex channel coefficient $h$ and the noise signal $n$ are normalized Gaussian random variable, i.e., distributed with $N(0, 1)$.